A Method for Obtaining Optimal Path in Angle and Avoiding Collision for Robotic Belt Grinding

Algorithm 1

Recurse search function (RobotTrackList).

	Extract the last node structure in the RobotTrackList, and get the variable i of this structure.
	IF (i = N)
	The track search is complete. The search function is terminated and returns to the function call point.
	ELSE
	Traverse all nodes of the (i + 1)^th column of the NodeMatrix. The total joint variation ∆θ of the robot grinding path is calculated when these nodes act as Nodei+1. The nodes of the (i + 1)^th column of NodeMatrix are sorted in ascending order of ∆θ.
	A variable k is created, and k = 1.
	Fork = 1 to M
	The k^th node of the (i + 1)^th column of NodeMatrix is searched. Make this node Nodei+1, and the intermediate nodes are   generated. Then, collision is detected for Nodei+1 and the intermediate nodes.
	IF (no collision occurs)
	The search function for this round is complete. Insert the Nodei+1 into the RobotTrackList at the end. Exit this function     and call for the next round of search.
	ELSE
	IF (k < M)
	Nodei+1 and the intermediate nodes in the RobotTrackList are abandoned.
	ELSE
	The algorithm cannot search the proper node from the (i + 1)^th column of NodeMatrix. Nodei, Nodei+1, and the     corresponding intermediate nodes of two nodes in the RobotTrackList are abandoned. The i^th layer of the search function is     terminated and returns to the (i − 1)^th layer of the search function.
	End
	End
	End
	End